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Energy 187 (2019) 115911

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Energy

journal homepage: www.elsevier .com/locate/energy

Multi-component energy modeling and optimization for sustainabledry gear hobbing

Qinge Xiao a, Congbo Li a, *, Ying Tang b, e, Jian Pan a, Jun Yu c, Xingzheng Chen d

a State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, Chinab Department of Electrical and Computer Engineering, Rowan University, Glassboro, NJ, 08028, USAc Applied Mathematics and Computer Science, Kyushu University, Fukuoka, 815-8540, Japand College of Engineering and Technology, Southwest University, Chongqing, 400715, Chinae Institute of Intelligent Manufacturing, Qingdao Academy of Intelligent Industries, Qingdao, 266109, China

a r t i c l e i n f o

Article history:Received 22 April 2019Received in revised form16 July 2019Accepted 7 August 2019Available online 8 August 2019

Keywords:Dry gear hobbingParameter optimizationEnergy modelingSustainable machining

* Corresponding author.E-mail address: congboli@cqu.edu.cn (C. Li).

https://doi.org/10.1016/j.energy.2019.1159110360-5442/© 2019 Elsevier Ltd. All rights reserved.

a b s t r a c t

Sustainable machining becomes a key priority for manufacturing industries due to the ever growingenergy costs, associated environmental impacts and carbon emissions. As one of the frequent activities inmetal machining, dry gear hobbing contributes to a significant portion of energy consumption. Processparameter optimization is an effective method of decreasing energy from process control perspective.However, hobbing parameter optimization is rarely involved in previous studies. To this end, a multi-component energy model is first developed on a basis of energy characteristics analysis of dry gearhobbing machines. Then, the optimization of hobbing parameters for the minimizing energy con-sumption and production cost is formulated as mathematical programming problem with a systematicconsideration of machining constraints. Finally, the optimization problem is solved by a modified multi-objective imperialist competitive algorithm (MOICA). The results demonstrate that the energy-efficientgear hobbing can be achieved through a collaborative effort of predictive modeling and parameteroptimization.

© 2019 Elsevier Ltd. All rights reserved.

1. Introduction

Manufacturing industry is facing economic challenges due tothe severe worldwide energy crisis and environmental pollution.Thus, sustainability of manufacturing systems needs to be putforward as one of the critical issues in the global agenda [1]. Ma-chine tools, which are highly widespread in manufacturing system,become the dominant electrical energy consumers with low energyefficiency [2]. Computer numerical control (CNC) machines, inparticular, have great potential in achieving sustainablemanufacturing due to their large portion (nearly 60%) of total en-ergy in machinery tool sectors [3]. These days, with the rapiddevelopment of automotive and aerospace industries, the demandfor gear hobbing machines is climbing, which nearly takes up 50%of the total gear cutting machines [4]. Activities related to gearhobbing would result in massive energy consumption, which mo-tivates researchers to seek effective sustainable strategies for the

large and growing number of gear hobbing machines.Dry gear hobbing becomes prevailing through a revolution of

wet hobbing by improving tool material and servo-driving tech-nologies [5]. Due to the disuse of coolant and lubricating fluid,hobbing process is much environmentally benign [6], however, inconjunction with some serious disadvantages such as lowmanufacturing precision [7], large tool wear [8], poor heat transfercondition [9] and huge energy consumption [10]. Hence, energy-efficient techniques incorporated with technological revolutionsare necessary for dry gear hobbing to keep the sustainablecompetitiveness. In relation to conventional machine tools, drygear hobbing machines hold unique characteristics in regard to thefollowing aspects. (i) Intricate generating motion of gear engagedwith hob causes stronger nonlinear and dynamic characteristics ofenergy. (ii) Multi-axes synchronous control in gear hobbing bringshigher request for energy decomposition. (iii) More auxiliarycomponents should be involved to assist the control and precisionpositioning, resulting in a large amount of parasitic losses. It ap-pears that dry gear hobbing is much complicated for its highbearing capacity, high driving capability and multi-componentmovements, which makes the development of sustainable

Q. Xiao et al. / Energy 187 (2019) 1159112

strategies a challenging issue.Process parameter optimization has been proved an effective

method of enhancing the machinability without significant hard-ware changes to the processes [11]. By varying the process pa-rameters such as spindle speed, feed rate and cutting depth,technologists attempt to maximize the overall benefits of themachining system. A perusal of the current literature suggests thatmost studies have been conducted on parameter optimization forconventional machining operations, such as turning [12], milling[13] and drilling [14]. In terms of gear hobbing, major efforts weremade with economic and technological considerations. Forinstance, Sant’Anna et al. [15] adopted Taguchi method to experi-mentally determine the optimal parameters for high productionefficiency. Similar work can be found in Zhang et al. [16] where theoptimizationmodel was establishedwith a physics analysis. For thepurpose of improving the gear precision, Sun et al. [17] used backpropagation (BP) neural network to establish a prediction model ofgeometric deviations. Yang et al. [18] developed a thermal energybalance optimization model for minimizing the average tempera-ture of cutting space. Karpuschewski et al. [19] conducted a study oftool life behavior dependent on cutting speed, where cost andproduction efficiency were both considered in optimizationcalculations.

Recently, sustainable gear hobbing begins to receive attention interms of process control, thermal energy analysis and low carbonemissions. Liu et al. [20] designed a fuzzy controller which regu-lates feed rate to reduce time and energy. As shown in their casestudy, 30.3% energy reduction was observed through the optimalcontrol. Li et al. [21] investigated the effect of hobbing parameterson thermal energy of spindle system, based on which an optimi-zation was performed with a result of reducing temperature andmaterial removal time by 11.6% and 48.8%, respectively. Cao et al.[22] proposed an optimization method to achieve high perfor-mance and low carbonmachining. They treated the gear hobbing asa black-box and optimized the process by supervised method. Theabove literature indicates that controlling hobbing parametersenhances energy efficiency. Despite this interest, the literature onparameter optimization for gear hobbing is rather scarce ascompared to optimization for other operations.

Another interesting observation from literature review is thatmost research on gear hobbing only partially concerns the energyabsorbed in material removal processes. As reported by Yoon et al.[23], this part of energy accounts for only a certain portion (nearly50%) of the overall energy. The machine components (e.g. servosystem, inverter, drive systems and spindle system) are also acti-vated in other machining periods, which results in a non-ignorableamount of energy consumption. As detailed decomposition of po-wer loss helps to improve prediction accuracy [24], researchersdevoted themselves to multi-component modeling of machinetools that were concentrated on spindle systems [25], feed drivesystems [26] and auxiliary systems [27]. These models can be usedto understand which component consumes the most energy inmachining process and can help manufacturers in design andproduction decision making. Apart from that, although thesemodels do not refer to energy modeling of dry gear hobbing ma-chines, they provide straight mathematical frameworks that can beextended to various operations.

For optimization purposes, techniques such as experimentaldesign [28], gray relational analysis [29], geometric programming[30], expert system [31] and heuristics [32] are intensively devel-oped to achieve energy conservation duringmechanical machining.Among the existing techniques, meta-heuristics are muchpreferred due to their better robustness and optimization effects[33]. In general, the parameter optimization problem is firstformulated as a constrained mathematical programming and then

the optimal solutions are obtained by iterative searching withheuristic strategies. Imperialist competitive algorithm (ICA) is anew evolutionary meta-heuristic algorithm inspired from thesocio-political process of imperialist countries to control morecolonies for strengthening their empires [34]. ICA shows superi-ority (e.g. computing time and quality of solution) to other well-known optimization techniques, which provides the basis of us-ing ICA-based method to solve the problem of parameter optimi-zation for dry gear hobbing.

Motivated by the above remarks, this paper aims to bridge theresearch gap and makes the following contributions. i) Differentfrom the studies that investigate the energy consumption from aspecific aspect, we attempt to construct a comprehensive modelintegrating all energy components of dry gear hobbing machine. ii)Since the energy-conscious hobbing parameter optimization is alarge-scale and highly constrained nonlinear optimization problem,a modified multi-objective ICA method is developed to resolve theissues of the unsatisfactory performance and low convergencespeed facing conventional optimization methods. iii) The complexinterplay of energy consumption and production cost with respectto hobbing parameters are explored to form the optimizationprinciples for sustainable dry gear hobbing.

With this basic positioning, the rest of the paper is organized asfollows. According to the energy characteristics analysis, acomprehensive energy model of dry gear hobbing is established inSection 2. The formulation of the multi-objective optimizationproblem and the description of the modified ICA are presented inSection 3. The modeling results and optimization performance arediscussed in Section 4, followed by conclusions in Section 5. Theschematic overview of the integrated modeling and optimizationmethod for sustainable dry gear hobing is depicted in Fig. 1.

2. Energy modeling of dry gear hobbing

The energy behavior of dry gear hobbing is much complicated.For better readability, the gear hobbing process is first given in Sub-section 2.1, followed by a description of multi-components prop-erty of energy consumption in Sub-sections 2.2. Then, the mathe-matical models from the view of energy breakdown are elaboratedin Sub-section 2.3.

2.1. Movements of gear hobbing

Gear hobbing is a process with intricate generating motion andmulti-axes synchronous machining. Fig. 2 is drawn to help under-stand the process well. In Fig. 2a, gear hobbing operation from anoverall perspective is depicted. The spindle motor-driven hob ro-tates with a spindle speed (n) around Y-axis and the gear rotatesaround Z-axis driven by the worktable with a certain speed (nt).Hob travels along the X-axis and Z-axis at certain feed speedsdenoted by Fx and Fz. The whole gear hobbing process is that thehob first travels from point A to point B along X-axis with slowfeeding Fx. Then, it moves along Z-axis at speed Fz and goes throughthe leading distance of the hob (BlT), the safe distance for theapproach (Ue), the safe distance for exiting (Ua) and the existingstroke (BoT). The hob travels from point C to point D with a quickfeeding and it finally comes back to the origin A, indicating thefinish of the processing.

Fig. 2b shows the detailed material removal process from hobcut in and out of the workpiece. When hob moves down to point A,the cutter edge just approaches the point N of the gear, repre-senting the start of a material removal process. The period of hobmoving from point A to point B is called cut in. In this period, theinterface of hob and gear becomes bigger and bigger, resulting ingradual increases of cutting force and power. The period of hob

Fig. 1. Overview of the whole paper.

Fig. 2. Graphic representation of the gear hobbing operation.

Q. Xiao et al. / Energy 187 (2019) 115911 3

moving from point B to C is called full cut, in which the teeth of hobinsert the gear completely. From point C to D, the period that hobmoves away from gear is called cut out. The cutting force and powercharacteristics in this period are opposite from what in hob cut-in.

2.2. Energy characteristics analysis

As with all the machine tools, each gear-hobbing machineconsists of multiple components, such as computers, coolant, feeddrives, motors, and spindle. Through the cooperation of the com-ponents in machine tools, a large amount of electricity is consumed

associated with cutting operations. Before establishing the energymodel, it is necessary to understand the energy composition anddistribution of gear-hobbing machines. Fig. 3a depicts the powervariation of a gear hobbing process. From the composition char-acteristics viewpoint, energy consumption (Eele) can be modeled asEq. (1) [35] where Est, Eu, Emr, and Ead denote standby energy, unloadenergy, material removal energy, auxiliary system energy andadditional load loss, respectively.

Eele ¼ Est þ Eu þ Emr þ Ead þ Eau (1)

Q. Xiao et al. / Energy 187 (2019) 1159114

Given that the energy can be calculated as a product of powermultiplies time, five corresponding power losses, i.e., standby po-wer (Pst) [36], unload power (Pu) [25], material removal power (Pmr)[37], additional load loss (Pad) [11] and auxiliary system power (Pau)[13], were well studied for conventional machining system. As forgear hobbing, unload power is produced under three conditions.The first one is the idling of the spindle that drives the hob. Thesecond one is the idling of the worktable. The third one is the stablerunning of the servo drive system without machining load. Ac-cording to general character of the unload power for CNC machinetools, unload power for a given gear hobbing machine is a functionof moving speed or rotation speed.

From a temporal characteristics viewpoint, the gear hobbingshows a fluctuating electric power demand that can be assigned todifferent operation states. Ignoring the power peak triggered by thestart/stop of machine components, the whole energy process canbe divided into several distinguishable states, i.e. standby period(tst), air-cutting period (tairc), cutting period (tcut). In each state,specific machine components are activated in cooperation tocomplete the required motions and thereby produce the energy oftime period. Then, the electricity can be generally formulated as:

Eele ¼ Est p þ Eairc p þ Ecut p (2)

where Est_p, Eairc_p, Ecut_p denote standby period energy, air-cuttingenergy, and cutting energy.

The above operation periods and the corresponding powerconsumption denoted by Pst, Pairc and Pcut are summarized asFig. 3b. It worth mentioning that the power consumed in idlingperiod (Pidle) is additional presented due to the fact that idling holdsan extremely short duration but it is important for acquisition ofmodel coefficients.

2.3. Multi-component energy models

2.3.1. Modeling of standby powerFollowed by the extremely short period of machine starts, the

gear-hobbing machine goes into the standby period. After that, thestandby power persists in the whole operation time. Due to the factthat there are several inverters and servers associated with thecollaborative and dynamic operation, standby power Pst is alwaysexpressed as:

Fig. 3. Power profile and energy constructio

Pst ¼ Paus þXM

Piinverter þXN

Pjdriver (3)

where Pinverter denotes the power of motor inverter, Pdriver denotesthe power of server, M and N are the number of inverters andservers, respectively.

2.3.2. Modeling of unload power

(1) Unload power of hob spindle (Psu)

The spindle system mainly consists of spindle motor, frequencyinverter and mechanical transmission. Each part consumes unloadpower and the corresponding power consumption is denoted byPsmotor , P

sinverter , P

stransmit . As indicated by Schudeleit et al. [27], the

unload power loss of mechanical transmission can be approxi-mated by a quadratic function in terms of spindle speed (n).

PSu ¼ PSmotor þ PSinverter þ PStransmit ¼ PSmotor þ PSinverter þ a1nþ a2n2

(4)

where a1 and a2 are the power coefficient of the mechanicaltransmission.

(2) Unload power of worktable (Ptu)

Similar to the spindle system, worktable rotation is driven byworktable motor, frequency inverter and mechanical transmission.In the hobbing process, spindle and worktable operate with aconstant transmission ratio, and thus the spindle speed (n) andworktable speed (nt) have the quantity proportion relation ofnt¼ nK/Zwhere K denotes hob starts and Z denotes number of teethof workpiece.

Ptu ¼ Ptmotor þ Ptinverter þ Pttransmit ¼ Ptmotor þ Ptinverter þ b1nt

þ b2n2t

¼ Ptmotor þ Ptinverter þb1KZ

nþ b2K2

Z2n2 (5)

where Ptmotor is the unload power of worktable motor, Ptinverter is theunload power of frequency inverter of worktable motor, Pttransmit isthe unload power of mechanical transmission. b1 and b2 are power

n of CNC high-speed dry gear hobbing.

Q. Xiao et al. / Energy 187 (2019) 115911 5

coefficient of the mechanical transmission of worktable.

(3) Unload power of Z-axis feed system (Pzu)

Feed systems are used to place the hob to the specified points.The Z-axis feed system drives the hob with the vertical movementsalong Z-axis. Different from the hob spindle and worktable, theunload power of mechanical transmission of feed system is foundto be a quadratic function of feed speed. Given that Z-axis feedspeed (Fz) and spindle speed (n) have a quantity proportion relationof Fz¼ fzKn/Z, the unload power of Z-axis feed system can be ex-presses as:

Pzu ¼ Pzservo þ Pzdriver þ Pztransmit ¼ Pzservo þ Pzdriver þ c1Fz þ c2F2z

¼ Pzservo þ Pzdriver þc1KZ

fznþ c2K2

Z2f 2z n

2 (6)

where Pzservo and Pzdrive is the unload power of Z-axis servo motorand servo drive, Pztransmit is themechanical transmission power of Z-axis driving motor, fz is the feed rate. c1 and c2 are the mechanicaltransmission loss coefficients.

(4) Unload power of X-axis feed system (Pxu)

The X-axis feed system, as the name suggests, is the system thatdrives the hob with the horizontal movements along X-axis. Theunload power of X-axis feed system is similar to that of Z-axis feedsystem and it can be generally expressed as:

Pxu ¼ Pxservo þ Pxdriver þ Pxtransmit ¼ Pxservo þ Pxdriver þ d1Fx þ d2F2x

(7)

where Pxservo is the unload power of X-axis servo motor, Pxdriver is theunload power of the servo drive, Pxtransmit is the mechanical trans-mission power of X-axis driving motor. d1 and d2 are the mechan-ical transmission coefficients.

2.3.3. Modeling of material removal power and additional load lossThe material removal power has been modeled through three

typical methods, i.e. specific energy based method, cutting forcebased method and exponential function based method. This paperadopts cutting force to calculate the material removal power forhigh accuracy, which is given by:

Pmr ¼ Fcv (8)

where Fc is the primary cutting force, and v is the cutting speed.As presented in literature [39], the cutting force in gear hobbing

can be approximated by an exponential model:

Fc ¼ KFmXF f YF

z εZF v�UF ZVF

.d (9)

where KF, XF, YF, ZF, UF and VF are the cutting force coefficients, m isthe normal modulus of hob, fz is the axial feed rate, ε is the ratio ofthe current cutting depth and the maximum cutting depth, v is thecutting speed of hob, d is the outer diameter of hob, Z is the numberof teeth of the gear. Among these parameters, m, d and Z can bepredetermined by tool specification.

In gear hobbing process, ε changes with the relation betweenhobbing depth (l) and maximum cutting depth (ap):

ε¼ l�ap; ap ¼ �

2h* þ c*�m� alp (10)

where h* is the addendum coefficient, c* is the dedendum coeffi-cient, and (2h*þc*)m equals to t as presented in Fig. 2b, alp is themachining allowance that remains for finishing.

Given that v ¼ pdn/1000, the material removal power can beobtained through combining Eq. (8), Eq. (9) and Eq. (10), as shownbelow:

PmrðlÞ¼ Fcv ¼ K0Fm

XF f YFz lZF n1�UF ZVF a�ZF

p d�UF (11)

Hobbing depth l2[0, ap] changes with the cut in and the cut outprocess of the hob. Thus, the material removal power as mentionedin Eq. (11) is modeled with the change of l. The calculation of thetime-varying l is shown in Eq. (12) obtained from a geometry point.

l¼ f ðtÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipðFztÞ2 þ qFzt þ s

qþw (12)

where t is the cutting time. p, q, s and w are coefficients of hobbingdepth.

The additional load loss has been proved to be a quadraticrelation of material removal power in CNC machining [38]. Thus,the additional load loss is estimated to be:

Pa ¼ e0P2c þ e1Pc þ e2 (13)

where e0, e1 and e2 are fitting coefficients.

2.3.4. Modeling of cutting time and air-cutting timeFrom the analysis in Section 2.2.1, the cutting length consists lAB,

lBC and lCD. Since lBC þ lCD exactly equals to the tooth thickness Bo,cutting time tcut can be expressed as:

tcut ¼ Lcut=Fz ¼ ðlAB þ BoÞ=Fz (14)

The invalid journey of hob along both X-axis and Z-axis is calledair-cutting. It can be seen from Fig. 2 that air-cutting exists in tra-jectory A-B-C-D-A. Since the air-cutting from point C to A is per-formed by fast feed, it can be ignored for its short duration.According to the above analysis of material removal process, theair-cutting length is the sum of L1, L2 and Ue. Then, the air-cuttingtime is given by:

tairc ¼ txairc þ tzairc ¼LxaircFx

þ LzaircFz

¼ L1Fx

þ Ue þ L2Fz

(15)

where Lxairc and Lzairc are the air-cutting lengths along X-axis and Z-axis, Fx is the X-axis feed speed, Fz is the Z-axis feed speed, L1 is thedistance between point A and point B, and L2 is the sum of Ua andBoT.

3. Multi-objective optimization of CNC high-speed dry gearhobbing

To achieve energy saving in dry gear hobbing, the optimizationvariables are first determined in Sub-section 3.1. The problem isthen formulated as a multi-objective mathematical programmingin Sub-section 3.2. Finally, a modified imperialist competitive al-gorithm is proposed to solve the problem as shown in Sub-section3.3.

3.1. Selection of optimization variables

As seen from the energy characteristics analysis above, the

Q. Xiao et al. / Energy 187 (2019) 1159116

power consumption during a gear hobbing process is mainlyaffected by hob spindle speed n, Z-axis feed rate fz, X-axis feedspeed Fx and cutting depth ap. The same may be said for productioncost. It should be noted that for the purpose of efficient produc-tivity, the cutting depth is always set nearly equal to the toothheight in dry gear hobbing due to the improvement of machinerigidity. Therefore, the controllable hobbing parameters (i.e. n, fz, Fx)are taken as optimization parameters.

3.2. Problem formulation of multi-objective optimization

The energy-aware optimization is made toward low energyconsumption (Etotal) and production cost (Cp) in pursuit of economicinterest and less energy use. An optimization model is proposed byconverting the problem into a constrained mathematical pro-gramming, as expressed in Eq. (16). The following gives descriptionof objectives F($) and constraints g($).

minFðn; fz; FxÞ ¼�minEtotal;minCp

�s:t: gðn; fz; FxÞ � 0 (16)

3.2.1. Optimization objectives

(1) Energy consumption

The energy objective, which is mainly concerned in this work.Besides of energy consumed in standby period, air-cutting periodand cutting period. The model also involves the tool changing en-ergy which consumes a certain portion of electricity. The overallenergy consumption is modeled as Eq. (17).

Etotal ¼ Pstðtst þ tctÞ þ�Psu þ Ptu þ Pxu þ Pzdriver þ

XM�2

Piinverter

þXN�2

Pjdriver þ Pauc þ Paus�txairc þ

�Psu þ Ptu þ Pzu þ Pxdriver

þXM�2

Piinverter þXN�2

Pjdriver þ Pauc þ Paus��

tzairc þ tcut�

þ Pcut�ap

� lBCFz

þð

tABþtCD

PcutðlÞdt

(17)

where tct is the tool changing time which can be calculated as Eq.(18) in which tptc denotes the per tool changing time, T denotes thetool life, CT, w and r are the tool life coefficients, and v is the cuttingspeed. Pcut is the cutting period power, which can be calculated asEq. (19).

tct ¼ tcutT

¼ tptctcutvwfrz

CT(18)

PcutðlÞ¼ Psu þ Ptu þ Pzu þ Pxdriver þXM�2

Piinverter þXN�2

Pjdriver þ Pauc

þ Paus þ PmrðlÞ þ Pa(19)

(2) Production cost

The production cost (Cp) for gear hobbing is composed by

overhead cost (Coverhead), cutting tool cost (Ctool) and electrical en-ergy cost (Cenergy).

Cp ¼Coverhead þ Ctool þ Cenergy ¼ k0Tp þ k1tpTþ k2Etotal (20)

where Tp is the processing time calculated by Eq. (21). k0, k1 and k2are cost coefficients.

Tp¼ tst þ tairc þ tcut þ tct ¼ tst þ LxaireFx

þ ZnfzK

Lzair þZ

nfzKLcut

þ tpctZTnfzK

Lcut

(21)

3.2.2. ConstraintsThe constraints of the optimization model are divided into three

groups. The first group (i.e. Eqs.(22)e(24)) refers to the referenceparameter boundaries provided by the tool manufacturers. Thesecond group (i.e. Eqs.(25)e(28)) is caused by the failure thresholdof system rigidity constrained by the performances of the machinesand the cutters. The third group relates to the requirement oftolerance and machining quality (i.e. Eqs.(29)e(31)). All constraintsare given as:

nmin �n � nmax (22)

fzmin � fz � fzmax (23)

Fxmin � Fx � Fxmax (24)

Pcut ¼ Psu þmaxðPmr þ PaÞ � hPe (25)

Tmin � CTvwf rz

(26)

KFmXF f YF

z v�UF ZVF

.2 � Mmax (27)

4com � 4space (28)

f 2z sina

4d� fcx (29)

p2mK2 sina

4Z,s2� fpx (30)

0:0321f 2zr

� ½Ra� (31)

where xmin and xmax (x¼ n/fz/Fx) are the lower and upper limits ofhobbing parameters, max($) is maximum function, the Pe is therated power of main motor, h is the motor efficiency, Tmin is theminimum values of the tool life, Mmax is the maximum torque ingear hobbing, 4com is the minimum temperature of compressed air,4space is the average temperature of cutting space under thermalenergy balance, a is the pressure angle, fcx is the required toothcurve error, s is the slot number of hob, fpx is the required toolprofile error, r is the hob nose radius and [Ra] is the requiredfinished surface roughness.

In the above mathematical expressions, Eqs.(22)e(24) specifythe safety range of hobbing parameters. Eq. (25) ensures that the

Q. Xiao et al. / Energy 187 (2019) 115911 7

maximum cutting power does not go beyond the product of powertransfer efficiency and rated power. To avoid the adverse effects ofhobbing parameters on tools and machines, Eq. (26) and Eq. (27)are set to ensure the choice of hobbing parameters satisfies thelimits of tool wear and spindle torque. Cooling effect should beadditional considered in high-speed dry gear hobbing, and thus Eq.(28) is used to ensure the temperature of compressed air neverexceeds the average temperature of cutting space. Readers arereferred to Yang et al. [18] for more details of 4space. To ensure themachining quality of dry hobbing process, tooth curve error, toolprofile error and surface roughness are constrained within requiredranges as shown in Eqs.(29)e(31), respectively. Note that Eq. (30) isadditionally arranged to regulate the tool selection for a requiredprecision, which thereby affects the setup of the rest of constraints.

3.3. Problem solving based on multi-objective imperialistcompetitive algorithm

ICA has gained widespread traction in the manufacturingdomain. A notable feature of ICA is the ease of performing neigh-borhood movements in continuous search space [40], whichexactly meets the requirements of parameter optimization in high-speed dry gear hobbing. To solve this issue, a modified multi-objective imperialist competitive algorithm (MOICA) is proposed,in which initial empires are reconstructed with the introduction ofdegree of constraint violation so that the searching process isassured on the feasible region. The assimilation and revolutionoperators are redesigned based on the Pareto-optimal mechanismto produce high quality solutions for trade-off optimization of en-ergy consumption and production cost.

Step 1: Initial empires

In this three-dimensional problem, a country is defined ascountry ¼ ðn; fz; FxÞT . N countries are first randomly generalized asinitial population P. For multi-objective optimization, the rank ofeach country is calculated by fast non-dominated sorting and non-inferior solutions h on the Pareto-optimal front are considered to berank 1. The cost of country represents quality of a solution, and thevalue is the small the better. With a consideration of machiningconstraints, the cost of the ith country (ci) is redefined as Eq. (32).

ci ¼u1ranki þ u2distim�

εþPl2Pranki

distlm�þ u3Gi (32)

Gi ¼XI¼J

j¼1

maxn0; gij

�ðn; fz; FxÞT

�o(33)

where ranki is the rank of the ith parameter solution according tonon-dominated sorting, distim is the crowding distance of solution iand m nearby solutions, Prankl is the solution set who belongs torank l, ε is a small positive number, Gi evaluates the constraintviolation degree, and J is the total number of constraints. u1, u2 andu3 are weight factors to tune the weight ratio of each item.

After calculating the cost of all countries, the proposed MOICAworks similar to the single-objective ICA. That is, Nim countries areselected from P to form initial empires and the N-Nim colonies areassigned directly proportionate to the power of empires. After that,

an imperialist composed of an empire and its colonies is con-structed. The calculation of power is set as Eq. (34).

pk ¼ cmax � ck þ xXNCk

g¼1

�cmax � cg

�(34)

where pk is the power of kth empire, NCk is the number of coloniesbelonging to empire k, cmax is the maximum cost among countries,and x is the power coefficient.

The steps of initialization can be summarized as Algorithm A.1.

Step 2: Assimilation

To enhance the power of imperialists, the original ICA imposesan assimilation policy so that colonies will move towards theirrelevant empire. In this movement, h and q are two randomnumbers subject to uniform distribution as illustrated in Eqs. (35)and (36) where d is the distance between colony and empire,b> 1 and 0< g<p are arbitrary numbers that randomly modify theposition of colonies.

h � Uð0; b�dÞ (35)

q � Uð�g;gÞ (36)

However, a noteworthy issue is that all the colonies around theempires try to be alike in assimilation, in the sense that doing sowill significant decrease the diversity of population and therebymake the optimization process in a fairly stagnant state. To over-come the mentioned limitation, we introduce differential evolution(DE) operator to realize communications among countries. The DE/rand/1 strategy works like that: for a machining scheme xi¼(xi,1, xi,2,xi,3), the adjacent solution z is generated as:

yj ¼ xr1;j þ F � �xr2;j � xr3;j

�(37)

zj ¼8<: yj ; if randð0;1Þ � CR or j ¼ jrand

xi;j; otherwise (38)

where r1sr2sr3si are randomly determined from P, CR is thecrossover probability, F is the scaling factor, and jrand is a randominteger ranges from Refs. [1,3], z¼(z1, z2, z3).

The proposed assimilation operator is shown as the pseudo codein Algorithm A.2.

Step 3: Revolution

Revolution operator in MOICA is another way to generate newcandidate solutions, which brings mutation (with a revolutionprobability UR) to a number of colonies in the search space to in-creases exploration and prevents the early convergence of coun-tries to local optima. We employ a polynomial mutation operator(Eq. (39)) to generate new machining schemes and replace themwith some colonies that have lower cost.

x0c;j ¼ xc;j þ d

�xmax;j � xmin;j

�(39)

Table 1Specifications of the gear machine, work piece and cutter.

Items Unit Numerical data

d ¼

8>><>>:

h2mþ ð1� 2mÞð1� d1Þhmþ1

i1=ðhmþ1Þ � 1; if m � 0:5

1�h2ð1� mÞ þ 2ðm� 0:5Þð1� d2Þhmþ1

i1=ðhmþ1Þ; if m>0:5

(40)

Q. Xiao et al. / Energy 187 (2019) 1159118

where m is a random number ranges from [0,1], d1 ¼ ðxc;j � xmin;jÞ=ðxmax;j � xmin;jÞ, hm is the distribution exponent. xmax,j and xmin,j arethe jth component of the solution.

The proposed revolution operator is depicted in Algorithm A.3.

Step 4: Imperialist competition

Competition is a process along with the collapse of the empiresand the redistribution of the colonies, which means that weakestcolony belonging to the weakest empire has greater probability tobe given to a stronger empire. The competition mechanism inMOICA requires a Probability Density Function (PDF). The posses-sion probability for the empire k is calculated by Eq. (41). Vector qwith the size of 1�Nim is form as Eq. (42). Then, vector D with thesame size of q is constructed by Eq. (43). Once the vector D iscalculated, the weakest colony is assigned to the empire that sat-isfies max

lfql � ulg. When an empire loses all of its colonies, it will

collapse and become one of the rest colonies.

qk ¼�����pk

,XNim

l¼1pl

����� (41)

q ¼ q1; q2; :::; qNim

(42)

D ¼ q1 �u1; q2 �u2; :::; qNim

� uNim

(43)

Machine toolRange of spindle speed [nmin, nmax](rpm) [0, 2000]Range of worktable speed [ntmin; n

tmax](rpm) [0, 300]

Range of X-axis feed speed [Fxmin, Fxmax](mm/min) [0, 3500]Range of Z-axis feed rate [fzmin, fzmax](mm/r) [0.7, 2.5]Standby power Pst(W) 2205

Step 5: Convergence

The proposed MOICA continues until: 1) predefined runningtime is met, or 2) there is only one grand empire remains. Other-wise, the method goes to Step 2.

Auxiliary power Pauc(W) 90Maximum modulus mmax(mm) 4Efficiency h 0.9Temperature of compressed air 4com

(�C) 15GearMaterial 20CrMnTi e

Modulus m(mm) 2Teeth number Z 51Tooth thickness Bo (mm) 35Pressure angle a(�) 20Required tooth curve error fcx(mm) 0.018Required tool profile error fpx(mm) 0.014Required surface roughness [Ra] (mm) 1.6Hob

4. Case study

This section discusses the proposed method for optimizinghobbing parameters to reduce the energy consumption of a realmachine tool. The experimental conditions are described in Sub-section 4.1. The coefficients of energy component model are esti-mated based on the experimental analysis in Sub-section 4.2. Thehobbing parameters are optimized for different objectives underthe given machining conditions, based on which the parametriceffects on energy and time are analyzed in Sub-section 4.3.

Material e High-speed steelModulus m(mm) 2Slot number s 3Number of threads K 3External diameter d(mm) 70Cutting depth ap(mm) 4.5Tool radius ra(mm) 0.2Helix direction - RightMinimum tool life Tmin(min) 560Per tool changing time tptc(s) 60Eq. (21) CT¼ 3� 108, m¼�1.9, r¼�1.91Eq. (24) k0¼ 0.3 ($/min), k1¼ 1600 ($), k2¼ 0.13($/

KWh)

4.1. Experimental setup

The experimental campaign is conducted on the YDE3120CNCdirect-driven high-speed dry gear hobbing machine. Gears made of20CrMnTi steel are machined by a hob that multi-layer coated withTiAlN. Table 1 lists the specifications of the primary components ofthe experimental setup and Fig. 4 shows the experimental setup inour case.

Through an analysis of NC programming, we have Z-axis air-cutting length Lzair of 21.168mm and X-axis air-cutting length of

104.5mm. Cutting length lAB þ Bo is 52.168mm, in which full cutlength lBC is 17.832mm. The instantaneous power demand of themachine components is accurately captured by the built-in powersensors. To read the process parameters associated with powerinformation of machine components in real time, an embodiedenergy monitoring system is developed. Working in a SIEMENSSinumerik Operate development environment, the energy moni-toring system communicates with CNC system through OPC UAprotocol and records power values. The cutting force is measuredthrough some additional experiments.

The modified MOICA algorithm parameters were set as follows:the number of populationN¼ 100, the number of empires Nim¼ 10,weight factors u1¼0.47, u2¼ 0.33 and u3¼ 0.20, the power coef-ficient x¼ 0.1, the scaling factor F¼ 0.3, the distribution exponenthm¼ 15, revolution probability UR¼ 0.02, and the crossover prob-ability CR¼ 0.9. Simulations for modeling and optimization areundertaken in Python 3.6.3 by a personal computer with Intel(R)Core(TM) i7-6700HQ CPU at 2.6 GHz with 8 GB of RAM.

4.2. Modeling results and validations

4.2.1. Energy modeling resultsTo model the unload power of spindle system and worktable, 9

Fig. 4. Dry gear hobbing process and power monitoring.

Table 2Experimental data for moving components.

Items Symbols Number

1 2 3 4 5 6 7 8 9

Spindle n/(rpm) 500 600 700 800 900 1000 1100 1200 1300Psidle/(W) 2330 2353 2379 2396 2429 2451 2480 2510 2547Psmotor þ Pstransmit /(W) 125 148 174 191 224 246 275 305 342

Worktable nt/(rpm) 30 60 90 120 150 180 210 240 270Ptidle/(W) 2254 2262 2275 2285 2299 2313 2325 2339 2357Ptmotor þ Pttransmit /(W) 39 57 70 80 94 108 120 134 152

X-axis feed Fx/(mm/min) 40 70 100 130 160 190 220 250 280Pxidle/(W) 2551 2569 2591 2622 2653 2681 2711 2729 2767Pxmotor þ Pxtransmit /(W) 346 364 386 417 448 476 506 524 562

Z-axis feed Fz/(mm/min) 60 90 120 150 180 210 240 270 300Pzidle/(W) 2725 2757 2778 2803 2822 2834 2860 2882 2914Pzmotor þ Pztransmit /(W) 520 552 573 598 617 629 655 677 709

Q. Xiao et al. / Energy 187 (2019) 115911 9

experiments are conducted. Since the idling power can be dividedinto spindle/worktable motor power, mechanical transmission andstandby power. The sum of motor power can be separated fromidling power. The experimental data is list in Table 2. Through leastsquares fitting, we have the model coefficients of Eqs. (4) and (5) as

Psmotor þ Pstransmit ¼ 46:2þ 0:121nþ 8:1� 10�5n2 (44)

Ptmotor þ Pttransmit ¼ 29:1þ 0:418nt þ 1:07� 10�4n2t (45)

Unload power of feed system is mainly related to feed speed.According to the energy characteristics analysis, the sum of servomotor power and mechanical transmission power can be obtainedby subtracting standby power from idling power of feed system.Based on Eqs. (6) and (7), the coefficients can be acquired as:

Pzservo þ Pztransmit ¼ 482:8þ 0:741Fz � 1:09� 10�5F2z (46)

Pxservo þ Pxtransmit ¼ 310:9þ 0:773Fx þ 4:37� 10�4F2x (47)

The coupling effects of spindle speed and Z-axis feed speed in-fluence material removal power. 9 orthogonal experiments areconducted according to L9(34). In the experiments, the threeparameter levels are chosen as n ¼ [640 rpm, 720 rpm, 800 rpm]

and Fz¼ [52mm/min, 58.8mm/min, 65mm/min]. For each exper-iment, cutting force and input power during cutting period aremeasured. The hobmoves along with the same parameters withoutmaterial removal to obtain the air-cutting power. Then, the sum ofmaterial removal power and additional load loss can be separatedfrom cutting period power by subtracting air-cutting power. Theexperimental combinations as well as the corresponding cuttingforce and power data are summarized as Table 3. Based on thecollected data, we obtained the coefficients of cutting force andadditional load loss as:

Fc ¼ 2:95f 0:65z ε0:81v�0:26 (48)

Pa ¼160:432� 0:076Pc þ 4:2� 10�5P2c (49)

Having obtained all the coefficients, we can easily establish thecomponent energy model by substituting the obtained equationsinto models in section 2.2.2 to 2.2.5. The overall energy model isthen constructed according to the framework described in Fig. 4.

4.2.2. Model validationsWe use ANOVA to check the fitness of component models to

experimental data. The analysis is carried out at the 95% confidenceinterval. Table 4 illustrates sum of the squares (SS), sum of the

Table 3Experimental data for material removal power and additional load loss.

No n/(rpm) Fz/(mm/min) fz/(mm/r) vc/(m/min) Pairc/(W) Fc/(kN) Pcut/(W) Pmr þ Pa/(W)

1 800 65 1.38 175.84 2925 0.947 5972 30472 720 65 1.53 158.26 2884 1.041 5895 30113 640 65 1.72 140.67 2851 1.158 5825 29744 800 58.8 1.25 175.84 2918 0.888 5770 28525 720 58.8 1.39 158.26 2889 0.978 5708 28196 640 58.8 1.56 140.67 2871 1.087 5655 27847 800 52 1.11 175.84 2886 0.822 5515 26298 720 52 1.23 158.25 2768 0.905 5367 25999 640 52 1.38 140.68 2755 1.003 5319 2564

Table 4ANOVA for the component models.

Eq. SS MS F-value P-value R2 R2-adj

(48) 42714 21327 2137.75 <0.0001 99.9% 99.8%(49) 10994 5482 1095.95 <0.0001 99.7% 99.8%(50) 29305 14652 400.34 <0.0001 99.3% 99.0%(51) 45184 22519 927.68 <0.0001 99.7% 99.6%(52) 33210 11070 597.89 <0.0001 99.4% 99.2%(53) 40294 20147 192.21 <0.0001 99.4% 99.2%

Q. Xiao et al. / Energy 187 (2019) 11591110

squares (MS), F-value, P-value, coefficient of determination (R2) andadjusted coefficient of determination (R2-adj). SS andMS reflect thetotal variation in data. That the greater F-values than critical Fcrit-ical¼ 5.14 indicates the strong statistically significant explanationcapacity of factors on responses. P-values are all smaller than 0.01,which reveals a good adjustment to the reality. Since R2 values arenearly in reasonable agreement with R2-adj and the values are allclose to 1, the models all show great prediction performance.

We use two performance metrics, i.e. t-test and prediction ac-curacy to test the overall energy model. The null hypothesis t-test[13] is used to validate the significance between the data calculatedby energy model and the one measured from experiments. Theaverage calculation accuracy (Acc) [37] is estimated to comprehendthe deviation extent. Seven sets of experiments under differentparameter combinations are conducted and the results are listed inTable 5. Note that the measured energy values are larger than thedata retrieved from energy monitoring system. This is because theactual measurements contain energy of startup period and spindleacceleration/deceleration which is ignored in the overall energymodel. The maximum Acc for the overall energy model and theproduction cost model are about 99.83% and 99.96%, respectively,which implies the obtained model is a good-fit one. In terms of t-test, we calculated the t score of the energy as 0.681 and the time as0.804. Since the two values are much smaller than the critical

Table 5Performance testing for the established models.

No. Obj. n (rpm) fz (mm/r) Fx (mm/min)

1 Etotal 900 2.0 20002 860 1.8 19003 820 1.6 18004 780 1.4 17005 740 1.2 16006 700 1.0 15007 660 0.8 14001 Cp 750 1.3 20002 900 1.6 15003 820 1.2 21004 995 1.4 18005 850 0.8 20006 1035 1.9 19007 1160 1.1 2000

tcritical¼ 2.446, the null hypothesis can be rejected. The statisticalanalysis shows that the energy and cost models provide goodprediction capabilities for optimization.

4.3. Parametric optimization for energy-efficient dry gear hobbing

On the basis of the predictive models, three sets of simulationswith a consideration of different objectives are conducted to verifythe necessity of multi-objective optimization. Besides, an empiricalscheme is added in the comparisons to show the superiority andpracticability.

Case 1. optimize the hobbing parameterswith the single objectiveof energy consumption.

Case 2. optimize the hobbing parameters for minimizing pro-duction cost.

Case 3. optimize the hobbing parameters for minimizing energyand cost concurrently.

Case 4. choose the hobbing parameters by personal experience orintuition of technologists.

4.3.1. Optimization resultsFig. 5 shows the evolutional process of population at the early,

middle and late stages. It can be clearly seen that at the early stage,the whole population is divided into 10 ranks through fast non-dominant sorting method. The line marked in red presents thesuperior individuals of the population at the current iteration. Onthe contrary, the absolute dominant solutions constitute the linemarked in blue. With the assimilation, revolution and competitionof countries in the MOICA, the Pareto optimum solutions for multi-objectives are achieved after enough generations of evolution.Then, the satisfactory solution is extracted through Analytic Hier-archy Process (AHP) method.

Predicted value Measured value Residual Acc

7.209� 105 7.221� 105 0.12� 104 99.83%7.169� 105 7.209� 105 0.40� 104 99.45%7.192� 105 7.231� 105 0.39� 104 99.43%7.292� 105 7.502� 105 1.10� 104 97.20%7.489� 105 7.691� 105 1.12� 104 97.37%7.821� 105 7.962� 105 0.91� 104 98.23%8.353� 105 8.413� 105 0.60� 104 99.29%0.6936 0.6977 0.0041 99.41%0.6561 0.6618 0.0057 99.13%0.6909 0.7023 0.0114 98.37%0.6532 0.6596 0.0064 99.03%0.8066 0.8173 0.0107 98.69%0.6693 0.6710 0.0017 99.74%0.6559 0.6681 0.0122 98.17%

Fig. 5. Non-dominant sorting of population in a) the 10th iteration, b) the 40th iteration, c) the 60th iteration and d) the 72nd iteration.

Table 6Optimization results with different optimization objectives.

Case n fz Fx Fz nt Energy/(J) Cost/($) T/(min) Tp/(s)

1 1495 2.50 2595.78 220.59 90 Etotal 209636.96 Cp 0.845 560.265 32.387Eair 36966.52 Coverhead 0.162Ecut 150114.84 Ctool 0.675Ect 56.98 Cenergy 0.0075Emr 106015.24

2 964 1.54 3000.00 87.427 58 Etotal 326377.13 Cp 0.654 2971.45 62.434Eair 63074.56 Coverhead 0.312Ecut 240775.31 Ctool 0.321Ect 27.11 Cenergy 0.0117Emr 132333.77

3 1083 2.50 2960.50 159.264 65 Etotal 235823.99 Cp 0.726 1006.99 39.765Eair 43373.06 Coverhead 0.199Ecut 171882.38 Ctool 0.521Ect 43.91 Cenergy 0.0086Emr 111997.26

4 900 1.3 2000.00 68.829 54 Etotal 369722.64 Cp 0.675 5285.452 82.4061Eair 79675.52 Coverhead 0.412Ecut 294351.58 Ctool 0.249Ect 20.97 Cenergy 0.0143Emr 141802.39

Q. Xiao et al. / Energy 187 (2019) 115911 11

Q. Xiao et al. / Energy 187 (2019) 11591112

Table 6 depicts the outcomes obtained through simulations.From the data, Case 3 compromises total energy and productioncost by 12.49% and 11.01% respectively, compared to their individ-ual minimumvalues. Even that, the proposedmethod decreases theenergy by 27.74% compared to Case 2 and decreases the productioncost by 14.08% compared to Case 1. Apparently, the production ef-ficiency oriented hobbing parameter optimization does not alwaysyield a solution that suits the need of energy saving. Therefore, themulti-objective optimization achieves the trade-off between con-flict objectives and the compromise of production cost is beneficialfor sustainable high-speed dry gear hobbing. As can be seen fromCase 4, the empirical scheme chooses conservative parameters forover-thinking the safety and other economic metrics comparedwith Case 3, so that the energy is observed a 56.71% increase eventhe production cost decreases by 7.55%.

To give an insight of the discipline of the parameter optimiza-tions, the decomposition analysis of energy and cost under theabove cases is conducted. It follows from Table 6 that cutting periodproduces the most portion (about 71.6%e73.7%) of the total energyconsumed in dry gear hobbing process. Among Ecut, the materialremoval energy occupies about 40.5%e50.6%. Due to the shortduration of air-cutting, the energy consumption only takes a certainproportion (about 17.6%e19.3%). Different from other conventionalmachining operations, the tool changing period only consumes0.6%e2.7% of the total energy for the long lifespan of hob. As forproduction cost, the overhead cost, cutting tool cost and electricalenergy cost share 19.1%e61.1%, 49.1%e79.8%, 0.9%e1.7% of the totalcost, respectively. Due to the high cost of hob, decrease of tool costshould be the primary consideration for reducing total cost.

For individually optimizing the energy consumption, relativelarge hobbing parameters are selected, which helps decrease theair-cutting energy and cutting energy significantly. Although thetool changing energy is increased, the obvious dropping tendencyof total energy is not affected for the small fraction of increase.However, selection of large cutting parameters lowers the tool lifein gear hobbing process, and as a result, tool cost related to tool life

Fig. 6. Contour plots of a)-c) energy con

is observed in an upward surge. Therefore, the production cost isalso increased in response to the rising tool cost. As for minimizingproduction cost, lower hobbing parameters are selected. Bydecreasing the spindle speed and feed rate, a 5 times improvementof tool life and a 29.2% reduction of cost are obtained with an in-crease in total energy by 55.6%. The satisfactory scheme acquiredthrough the proposed MOICA method chooses a moderate spindlespeed to address the energy concerns together with the objective ofcost. Empirical hobbing uses small parameters to prolong the toollife up to 5285.4min, which in turn shows increases in processingtime and total energy.

4.3.2. DiscussionsThe contour plots for the measured responses help to under-

stand the variation tendency of energy consumption and produc-tion cost with hobbing parameters in dry gear hobbing. Fig. 6 isdrawn for several scenarios where any two hobbing parametersvary within the target ranges while another one is kept constant.The red points represent the Pareto solutions obtained byMOICA. Itcan be inferred that heavier cutting conditions benefit energysaving due to the significant decrease in processing time. Thus, lowenergy consumption in gear hobbing process is also desirable forhigh efficient machine tools. However, contour graphs (Fig. 6 d ande) showa different trend for the objective of production cost. Fig. 6edepicts that production cost first decreases and then slight increasewhen increasing Z-axis feed and keeping spindle speed to 1083 r/min. The similar effect is observed in Fig. 6f that the production costdecreases first and then rises with the increase of spindle speed.Intensive degree of contour lines reveals the impacts of hobbingparameters. It follows that spindle speed and Z-axis feed rate arethe most influential parameters for the total energy consumptionand production cost, while the impact of X-axis feed speed is minor.This is because X-axis feed speed only affects air-cutting time andenergy which occupies low proportion of Tp and Etotal, respectively,on the contrary, spindle speed and Z-axis feed rate are stronglyrelated to cutting energy and tool life.

sumption and d)-f) production cost.

Q. Xiao et al. / Energy 187 (2019) 115911 13

Fig. 7 describes non-linear variation of total energy, productioncost and processing time as the hobbing parameters increase. Allenergy and production lines show the downtrend on processingtime and total energy with increasing hobbing parameters. Fromthe energy composition perspectives (Fig. 8a and b), cutting energyand air-cutting energy are descending with the increases of spindlespeed and feed rate while tool changing energy increases withoutsignificant changes. It can be concluded that to improve energyefficiency and time efficiency, maximum parameters withinacceptable ranges should be selected. Also, time and energy do notpossess a trade-off relationship between them in dry gear hobingprocess. Fig. 7a shows that as the spindle speed increases from 0 to600r/min, the production cost has a slight decrease from 0.661$ to0.654$, which suggests that the overhead cost dominants tool costin this range. When spindle speed is beyond 600r/min, themachining schemes start to enter the range of Pareto-optimality.The tool cost turns to be a sharp increase associated with the in-crease in production cost. This trend can be verified through anobserved non-dominant solution to Case 3, as presented in Fig. 7a.From the cost component perspectives (Fig. 8c and d), the upgraderate of tool cost gradually dominants the reduction rate of overheadcost and energy cost with the increases of spindle speed and Z-axisfeed rate. Similarly, the inflection points can be found asfz¼ 1.3mm/r and Fx¼ 2650mm/min. This phenomenon is alsoproved through non-dominant solutions obtained from the Paretofront as shown in Fig. 7b and c.

4.3.3. Thermal analysis of optimization resultsDue to the poor heat transfer condition of dry gear hobbing,

cutting heat cannot be immediately dispatched, leading to anaccumulation of the thermal energy in cutting space that will doharm to the machinability [41]. Thus, how parametric optimizationbrings about the variation in temperature of cutting space is the

Fig. 7. Effects of a) spindle speed, b) feed rate and c) X-axis feed

main concern of this section. A set of temperature rise tests wereconducted for cases with different optimization objectives. Thedata of temperature within the cutting space were continuouslycaptured with a frequency of 2 s.

Fig. 9 depicts the temperature variation of average temperatureof cutting space (4space) from heat balance state to end of gearhobbing. In actual practice, the increase of 4space at the relativelyfixed level of workshop ambient temperature would cause me-chanical components expansion and thereby decreases themachining precision. Compared with the curves of temperaturevariation in Fig. 9, one can find that different parameter schemesresult in significant differences in 4space. Case 1 is with the lowest4space followed by Case 3, Case 2 and Case 4. Note that for batchprocessing, it occurs temperature jump in part changing processes.Temperature jump is much remarkable when using hobbing pa-rameters in Case 2 and Case 4 while the effects are weakened inCase 1 and Case 3. This demonstrates that large spindle speed andZ-axis feed rate are beneficial for decreasing average temperatureof cutting space. In dry gear hobbing, 4space is tightly associatedwith the heat transfer capacity since almost 75% of heat is trans-ferred by cutting chips while air compressor only transfers about10% heat. Spindle speed and feed rate determine the materialremoval rate. As the spindle speed and feed rate increase, the morematerial is removed and hence the more heat generated fromcutting area can be dispatched through cutting chips. The resultshow an exactly consistent trend to the conclusion that largespindle speed and feed rate should be selected when to pursuitenergy conservation. This means that high material removal ratereduces energy consumption together with the effect of thermaldeformation, giving better machinability for dry gear hobbing. Onthe contrary, empirical hobbing (Case 4) chooses a relatively lowparameters with an excessive consideration of safety, cost orquality. However, high 4space is observed, indicating that parameter

speed on total energy, production cost and processing time.

Fig. 8. 3D surface plots for interaction effects associated with spindle speed and feed rate with regard to a)-b) energy and c)-d) cost.

Fig. 9. Variation of temperature in cutting space under different cases.

Q. Xiao et al. / Energy 187 (2019) 11591114

selection by personal experience and intuition increase the possi-bility of thermal deformation and thus cannot meet the require-ment of sustainable dry gear hobbing.

4.3.4. Comparative test of MOICATo evaluate the performance of the proposed algorithm in

solving the gear hobbing optimization problem, the proposedMOICA is compared with three typical heuristic algorithms, i.e.

Q. Xiao et al. / Energy 187 (2019) 115911 15

non-dominated sorting genetic algorithm II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and multi-objective evolutionary algorithm based on decomposition (MOEA/D). Each algorithm is taken 10 times runs to validate the consis-tency in generating Pareto fronts. Three Pareto evaluation metrics,i.e. Hypervolume (HV), Inverted Generational Distance (IGD) andSpread (D), are adopted to measure the multi-objective optimiza-tion performance. Besides, the running time of CPU is also evalu-ated in the comparison. Table 7 shows the results of MOPSO, NSGA-II, MOEA/D and MOICA, where the best, worst, mean and standarddeviation are reported.

From Table 7, NSGA-II has the best HV but MOICA succeeds tofind the best worst, best median and best standard deviation HVvalues, which indicates the improved proximity and diversity ofMOICA over the other three algorithms. MOPSO obtains better bestIGD values than MOICA. Nevertheless, MOICA outperforms NSGA-IIand MOEA/D by obtaining the best worst and best median values.All the worst IGD values reveal that MOEA/D fails to find a goodapproximation and coverage of the PF*. MOICA performs consis-tently better than the other three algorithms in terms of D, exceptthe worst value, which shows MOICA is able to find widelydistributed solutions. The advantage of MOICA andMOPSO in termsof running time of CPU is obvious in this problem. These two al-gorithms have a similar performance on convergence efficiency butMOICA hasmore stability of fast generating Pareto-optimality front.Generally speaking, we can conclude from the different obtainedresults that MOICA performs the best among the compared algo-rithms in dealing with energy-oriented hobbing parameteroptimization.

5. Conclusions and future work

In this paper, we proposed a new component-based modelingmethod of energy consumed in high-speed dry gear hobbing. Onthe basis of the obtained models, parameter optimization wasconducted to minimize energy consumption and production cost.Case study was presented to demonstrate the effectiveness offinding the trade-off between energy conservation and productioncost reduction.

The results show that energy, processing time and productioncost are directly affected by the hobbing parameters. There is noobvious trade-off between processing time and energy while en-ergy and production cost are in conflict with each other. Spindlespeed and Z-axis feed rate are two critical variables to the threeobjectives. Selection of large spindle speed and large Z-axis feedrate is beneficial for reducing time and energy, but it would shorten

Table 7Performance comparisons among MOICA and other algorithms.

Metrics Algorithm Best Worst Mean Std.

HV MOPSO 0.8851 0.8778 0.8808 0.0033NSGA-II 0.8857 0.8739 0.8803 0.0029MOEA/D 0.8814 0.8566 0.8714 0.0102MOICA 0.8852 0.8784 0.8813 0.0027

IGD MOPSO 0.0012 0.0016 0.001453 0.000144NSGA-II 0.0013 0.0017 0.001533 0.000137MOEA/D 0.0014 0.0018 0.001602 0.000149MOICA 0.0013 0.0016 0.001450 0.000138

D MOPSO 0.6932 0.8345 0.755733 0.058418NSGA-II 0.6642 0.8094 0.739225 0.060978MOEA/D 0.7031 0.8212 0.800067 0.061095MOICA 0.6641 0.8095 0.721242 0.055182

Time (s) MOPSO 5.2871 5.3432 5.31491 0.01419NSGA-II 5.6372 5.8933 5.77776 0.09598MOEA/D 5.6645 5.8958 5.76200 0.09546MOICA 5.2872 5.3214 5.30217 0.01418

the tool life and increase tool cost. Moderate spindle speed and highfeed rate help to reach green and low cost dry gear hobbing.

The research can be extended in several directions. For instance,intelligent methods are supposed to be developed to furtherimprove the convergence rate of the algorithms. Due to the heavytool wear in dry gear hobbing process, embodied energy can be alsoconsidered for better achieving sustainablemachining. Factors suchas temperature, vibration and surface state may also affect powerloss. Thus, it is necessary and challenging to refine our predictivemodel by adding the above factors.

Declaration of interests

The authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper.

Acknowledgements

This work was supported in part by the National Natural ScienceFoundation of China (No. 51975075), Chongqing Technology Inno-vation and Application Program (No. cstc2018jszx-cyzdX0146) andthe Fundamental Research Funds for the Central Universities ofChina (No. cqu2018CDHB1B07).

Appendix A. Supplementary data

Supplementary data to this article can be found online athttps://doi.org/10.1016/j.energy.2019.115911.

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